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  • Three capacitors of capacitance , gut. and c are connected once in series and a

Three capacitors of capacitance 3 \mu \mathrm{f}, gut. and c are connected once in series and another time in parallel. The ratio of equivalent capacitance in the two cases \left(\frac{C_s}{C_p}\right) will be -

Option: 1

1:15


Option: 2

15:1


Option: 3

1:1


Option: 4

1:3


Answers (1)

best_answer

\mathrm{Given, \begin{aligned} & c_1=3 \mu \mathrm{f} \\ & c_2=\operatorname{5\mu f} \\ & c_3=1 \mathrm{5 \mu f} \end{aligned} }
\mathrm{Case I\, All \, \, are \, \, in\, \, series- \begin{aligned} & \frac{1}{c_s}=\frac{1}{3}+\frac{1}{9}+\frac{1}{18} \\ & \frac{1}{c_s}=\frac{6+.2+1}{18}=\frac{9}{18} \\ & \frac{1}{c_s}=\frac{1}{2} \Rightarrow c_s=2 \mu \mathrm{F} \end{aligned} }
\mathrm{Case\, \, II\, \, All \, \, \, are \, \, in\, \, parallel- C_p=3+9+10=30 \mu \mathrm{F}}

\mathrm{Now, \left(\frac{C_S}{C_p}\right)=\frac{2 \mu \mathrm{F}}{30 \mu \mathrm{F}}=\frac{1}{25} \text { An } option-A}

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jitender.kumar

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